Question: Solve for $x$ and $y$ using elimination. $\begin{align*}5x-8y &= 4 \\ -5x+6y &= -8\end{align*}$
Solution: We can eliminate $x$ when its corresponding coefficients are negative inverses. Add the top and bottom equations. $-2y = -4$ Divide both sides by $-2$ and reduce as necessary. $y = 2$ Substitute $2$ for $y$ in the top equation. $5x-8( 2) = 4$ $5x-16 = 4$ $5x = 20$ $x = 4$ The solution is $\enspace x = 4, \enspace y = 2$.